# DESIGN AND ANALYSIS OF ALGORITHMS: INTRODUCTION. DESIGN and ANALYSIS of ALGORITHMS.

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DESIGN AND ANALYSIS OF ALGORITHMS: INTRODUCTION

DESIGN and ANALYSIS of ALGORITHMS

 al-Khw ā rizm ī : Persian mathematician, astronomer  “On the calculation with Hindu numerals”; 825 AD decimal positional number system ALGORITHMS ZERO (500 AD)

ALGORITHMS  algorithm  recipe  an effective method expressed as a finite list of well-defined instructions for calculating a function  Formally, algorithms are Turing machines BISI BELE BATH Take rice and dal, wash and soak for 10 min. Soak tamarind in water; extract juice Cook the dal till it is half done Roast the spices. Mix them with coconut; add turmeric powder,. Grind mixture into a thick paste using a little bit of water. Heat oil in pan. Burst mustard seeds and add curry leaves. Add onions and stir fry till soft. Add tamarind juice and 2 cups of water to the onions and bring to boil. Add rice, vegetables, tomatoes, half-cooked dal, spice mixture and salt. Cook on a low flame till done. Garnish with coriander leaves. Source: Wikipedia

ALGORITHMS In this course:  Instructions are basic instructions a computer can do.  However, we will be independent of programming languages/architectures/machines.  Imperative programming. Computational problem to solve Computational problem to solve Algorithm Program Design & Analysis Programming

DESIGN PARADIGMS Design paradigm: An underlying design principle that forms the basis of many algorithms. Example: Towers of Hanoi / Brahma cone Design principle: Recursion / divide-and-conquer When subproblems merge: dynamic programming

DESIGN PARADIGMS  Brute force  Divide and conquer  Dynamic programming  Greedy method  Decrease and conquer  Transform and conquer (aka reductions)

TYPES OF PROBLEMS  SORTING  SEARCHING  STRING PROCESSING  GRAPH PROBLEMS  COMBINATORIAL PROBLEMS  GEOMETRIC PROBLEMS  NUMERICAL PROBLEMS

UI NET- WORK ALG LIBRA -RIES DB WEB FILE MGMT ALGORITHMS AND SOFT. ENGG. SYSTEM WEB SEARCH: google/bing key algorithms: indexing for fast search; ranking. THIS MEC SYSTEM: video key algorithms: mp4 compression

ALGORITHM DESIGN AND ANALYSIS  CORE OF COMPUTATIONAL THINKING Useful for your entire career as a computer engineer.

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